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We study the asymptotics for $${\\mathbf {P}}(M_\\tau >x),$$<\/jats:tex-math>\n \n P<\/mml:mi>\n (<\/mml:mo>\n \n M<\/mml:mi>\n \u03c4<\/mml:mi>\n <\/mml:msub>\n ><\/mml:mo>\n x<\/mml:mi>\n )<\/mml:mo>\n ,<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> as $$x\\rightarrow \\infty $$<\/jats:tex-math>\n \n x<\/mml:mi>\n \u2192<\/mml:mo>\n \u221e<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s11134-020-09661-z","type":"journal-article","created":{"date-parts":[[2020,6,23]],"date-time":"2020-06-23T11:02:52Z","timestamp":1592910172000},"page":"211-223","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Maximum on a random time interval of a random walk with infinite mean"],"prefix":"10.1007","volume":"98","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0025-7140","authenticated-orcid":false,"given":"Denis","family":"Denisov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,23]]},"reference":[{"key":"9661_CR1","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1214\/aoap\/1028903531","volume":"8","author":"S Asmussen","year":"1998","unstructured":"Asmussen, S.: Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities. 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